Russell Cheng's Home Page
[Last
update:Dec 2002]
Contact
Information
Faculty
of Mathematical Studies,
Tel:
+44 (0)23 8059 4550 (direct), 8059 5155 (OR secretaries)
Fax:
+44 (0)23 8059 5147
email:
rchc@maths.soton.ac.uk
Brief
CV
Russell
C.H. Cheng is Professor of Operational Research in the Faculty of Mathematical
Studies,
He has
an M.A. and the Diploma in Mathematical Statistics from
Research
Interests
I have
divided my Publication List
into
the six main areas that I have been interested in. My main current areas of
interest are 2. Design and
Analysis of Computer Simulation Experiments, and 4. Estimation in Non-Regular Problems
Here
is a brief description of each. Click on linked items to jump straight to them
in the list.
Commentary on Publication list:
1. Computer
Generation of Random Variables
From
1976 to 1984 there was considerable interest in the development of computer
methods of generating random variables from various probability distributions,
notably the so-called gamma and beta distributions. The better current
implementations date from that time, but be warned there are still books being
written, and implementations using outmoded, demonstrably inferior, methods
from before then. If you want something neat and simple then [A1,A2] and those
[A3,A4]
with Feast ( a research assistant at the time) are methods that I am most
pleased with.
If you
want cookbook recipes then try my Chapter on Random Variate Generation. This
appears in A7 Handbook of Simulation, edited by Jerry Banks and published by Wiley in 1998.
2. Design and
Analysis of Computer Simulation Experiments
I have
several current research interests in this area: optimal design, selection of
input models, validation and sensitivity analysis.
The
papers [B2, B3]
jointly with Feast were the first to investigate the use of control variables
under normality assumptions. This is a common assumption nowadays.
The
method of antithetic variates is well known in theory, but is not so easy to
apply in practice. The papers [b1,b2 B4,B5] develop a practical
methodology for its application from a novel viewpoint. Paper [b3], is expository, but
suggests a structure for the methodology of variance reduction. The conference
paper [a1][, gives an implementation of quasi-random generators.
The
papers [A5, A6],
though concerned with variate generation, would find application in variance
reduction In particular [A5] contains a result concerning the decomposition of
inverse Gaussian variates.
Paper
[b4],
is concerned with some unusual ways of doing stratified sampling.
Paper
[B6]
with
Most
recently I have worked with a research student, Traylor, and a colleague,
I have
also been working on sensitivity issues with Prof Jack Kleijnen (
3. Construction
of Confidence Bands
The
basic idea of constructing confidence bands dates back to the work of Working
and Hotelling in 1927. However the idea can be extended non-trivially. Paper [C2] with Iles
gives convenient closed form formulas for a problem a number of well known
distributions. Papers [C3,C5,c1,c2] describe some
of the work done for the MoD in this area, as well as applications to materials
handling. The methodology developed in paper [C3] is capable of wide
application.
4. Estimation
in Non-Regular Problems
This
is technically the most demanding area that I have worked on. It concerns a
number of problems in which the well-known and the normally powerful method of
maximum likelihood can fail to provide estimators with good properties. The
papers [D1,D2,D3,D4,D5,D6] address a
notorious outstanding problem where the likelihood blows up and such estimators
are inconsistent. The joint paper [D2] with Amin (a research student at the
time) gives what I consider to be a natural and practical solution using
spacings that is demonstrably superior to previous suggestions. The joint paper
[D4] to some extent gives a unifying explanation of why certain methods work
and why others do not for such problems. Paper [D6] proves a remarkable
property of the spacings method that has uses in goodness-of-fit testing. The
joint papers [D7,D8] tackle a
second problem of non-regularity that occurs in estimation and in curve fitting
respectively. Each paper gives a new characterization of the difficulty, and
each shows how the problem can be fully solved. This work lead to the a read
paper to the Royal Statistical Society [D10].
Papers
[D9, D11] is recent
work on this with Steve Liu from
5. Optimal
Control of Jump Processes
The
papers [E1,E2],[e1] and those [E3,E4] jointly with
Jones (then a part-time student) attempt to model the operation and control of
large scale chemical plants using Markov Decision Processes. The purpose is to
develop a practical solution to a problem of industrial interest which is
analytically intractable except in simplistic rather trivial cases. Paper [E2]
establishes, in fair theoretical detail, conditions under which the technique
can be expected to work. As [E3] and [E4] go on to show, the practical results
agree with the theory. The topic has been relatively unexplored, with what
published work being dispersed.
Relatively
recently I returned to the problem and [E5] contains a detailed
theoretical analysis using the theory of maximal differential equations.
6. Computer
Generated Imagery Techniques and Marine Simulation
I have
developed a number of computer algorithms over several years in my consultancy
work on applications of computer generated imagery in marine simulation. These
have had real and I held two Teaching Company Grants from the EPSRC in this
field; each Scheme included a specific research component in addition to the
usual commercial ones. Some results of this work are reported in [f2, f3, f4].
Perhaps
more interesting are the papers [F1, F2]. Paper [F1], though
short, gives a new rendering method that is demonstrably two to three times
faster than previously suggested methods. Paper [F2] gives a comprehensive
solution to the problem of fast anti-aliasing. Both methods have been used in
several extremely successful commercial systems.
Some
Teaching Materials
